1. Field of the Invention
The present invention relates to a method and computer program for shared estimation of parameters, in particular to the determination of “Error Vector Magnitude” (hereinafter “EVM”).
2. Description of the Background Art
The “Error Vector Magnitude” (EVM) is used often, to estimate the linearity of a digitally modulated mobile radio system. For Example, the standard “GSM 05.05, version 8.5.0, Draft ETSI EN 300 910 V.8.5.0, (2000–07), Annex G” (hereinafter “the standard”) defines the requirements on the EVM for the 8-PSK GSM EDGE-System. However, the standard does not define algorithms in order to determine the EVM.
FIG. 1 shows an example configuration, in accordance with the above given standard, of a transmission channel 20 having different parameters ε, w, C1, and C0. The parameter ε represents a time shift, that determines the signal in the delay 21 of the configuration, e(k) is an error vector which is added in the configuration in a adder 22, C1 is a complex amplification which is added in the multiplier 23, and C0 represents a constant level of a DC-offset. The parameter Wk is used to model the time response during a burst (transmit block), for example due to a heating up of the amplifier.
The following allocations are applied:    Ts: symbol period;            The sequence of the configuration, are present before the symbol clock of the time points kTs.            s(k): reference signal: is a trouble-free input signal after the measurement filter in the receiver to the symbol-time points kTs;    e(k): error vector;    ε: resultant time shift due to a non-ideal estimation of the preceding coarse time shift estimation;    C1: complex amplification (gain) of the measurement signal;    C0: constant level of a (DC) offset in the measurement signal; and    w=eα+jΔωTs α describes the change in amplitude of the measurement signal, which, for example, because of the heating up of the amplifier, causes a higher signal level to arise within the bursts.            Furthermore, through Δω the resultant frequency shift is modeled due to the preceding non-ideal coarse frequency estimation.        
From the reference signal s(k), the following received signal z(k) results:z(k)={C0+C1·[s(k)+e(k)]}·wk.  (1)
The error vector e(k) is determined by:
                              e          ⁡                      (            k            )                          =                                                            z                ⁡                                  (                  k                  )                                            ·                              w                                  -                  k                                                                    C              1                                -                                    C              0                                      C              1                                -                                    s              ⁡                              (                                  k                  -                  ɛ                                )                                      .                                              (        2        )            
In view of this model, a total of seven real parameters have to be estimated. It is noted that the time shift ε, in view of the excessive sampled sequence, is to be understood to fulfill the sample theorem.
The “Error-Vector magnitude” (EVM) is calculated over a burst and is defined as follows:
                    EVM        =                                                            ∑                k                            ⁢                              |                                  e                  ⁡                                      (                    k                    )                                                  ⁢                                  |                  2                                ⁢                                  /                                      ∑                    k                                                  |                                  s                  ⁡                                      (                    k                    )                                                  ⁢                                  |                  2                                                              .                                    (        3        )            
To determine the “Error-Vector magnitude” (EVM), the parameters ε, C0, C1 and w, must be estimated such that a minimum of the “Error-Vector magnitude” (EVM) per burst results. Through the use of this parameter, the individual error vector e(k) can be calculated for each symbol.
The article “A Method for Computing Error Vector Magnitude in GSM EDGE Systems—Simulation Results,” IEEE Communications Letters, VOL. 5, NO. 3, March 2001, pages 88 to 91, discloses a method to determine the parameters ε, C0, C1 and w. This conventional method is, however, not very efficient. For one, the conventional method has the disadvantage that the time shift ε is not subjected to a common estimation with the parameters C0, C1, and w, but that only a coarse estimation of the time shift ε is performed before the common estimation of the parameters C0, C1 and w. Moreover, the conventional method has the disadvantage that a gradient method has to be used, which converges relatively slowly. The conventional method requires therefore, a relatively large number of iterations, which are dependent on the arbitrary start values for C0, C1 and w.